Exponents

Welcome! I'm excited to help you learn about exponents as easily as possible. There's a lot to learn, so I've created several pages with step-by-step examples and explanations.

This page is a "table of contents" page so you can find the specific topic you're looking for. I hope it's helpful for you and that these pages make it easy to learn about exponents. Good luck!

What is an exponent?

The exponent is the small number in the top right hand corner. 

The base is the larger number at the bottom of the exponent.

The combination of an exponent and a base is called a power

If this is your first time learning about exponents, read this page about how to simplify positive exponents

Types of Exponents

Positive exponents are the most common type of exponent and they're the easiest to simplify. Exponents of 0 and 1 are also super easy.

Negative and fractional (or rational) exponents are a little more challenging but once you learn the rules, they're not too bad. 

Click on the buttons below to see how to work with each type of exponent...


Exponent of 0

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Exponent of 1

Click Here

Positive Exponents

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Negative Exponents

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Fractional Exponents

Click Here

Types of Bases

Most of the time, the base of the power will be a positive number or a variable. But sometimes, you may have a base that's a little more difficult to simplify...like a negative number, a fraction, a complex number, or a polynomial

Click on the buttons below to see how to work with each type of base...


Negative Numbers

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Fractions

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Complex Numbers

Click Here

Variables

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Binomials

Click Here

Polynomials

Click Here

Exponent Rules

The exponent rules can be used to simplify exponential expressions. Click on the buttons below to see examples of how each rule works...


How to Use the Exponent Rules

Click Here

Product Rule

\(x^{a}x^{b}=x^{a+b}\)

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Quotient Rule

\(\frac{x^{a}}{x^{b}}=x^{a-b}\)

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Power Rule

\((x^{a})^{b}=x^{ab}\)

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Negative Exponents

\(x^{-a}=\frac{1}{x^a}\)

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Rational Exponents

\(x^{\frac{a}{b}}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a\)

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Distributive Property of Exponents (x and \(\div\)) 

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\((xy)^a=x^a y^a\)

\((\frac{x}{y})^a=\frac{x^a}{y^a}\)

Exponential Functions & Equations

Exponents are a pre-requisite for high school math classes. In high school, you may be asked to solve an exponential equation.

You could also be asked to write an exponential function (or graph it).

Or you may work with polynomials and rational functions, which use exponents on a regular basis. 

Click on the buttons below to learn more about these related topics... 

Exponential Equations

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Exponential Functions

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Exponential Graphs

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Polynomials

\(5x^3-4x^2+7x-9\)

Click Here

Rational Functions

\(\frac{4x^2-9x+3}{5x^3-8x+6x-1}\)

Click Here

Resources

Free Printable Worksheets
& Online Practice Problems

When you scroll to the bottom of each of the pages linked above, you'll find links to free printable worksheets and free online practice problems to help you practice each concept. 

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